Statistical significance & the Normal Curve

What tools have we used? Measures of Central Tendency Mean, median, mode Measures of Variation Range, standard deviation, variance

When is a difference reliable? When the sample is REPRESENTATIVE, not BIASED Random sample, random assignment When the observations are less variable, rather than more variable Are there major outliers? Etc. More cases, rather than fewer Once we know sample is representative, you want more cases Difficult to bring clout to findings of 3 people vs. 50,000 people

Statistical significance “a statistical criterion for rejecting the assumption of no differences in a particular study The likelihood that a result or relationship is caused by something other than mere random chance Statistical hypothesis testing is traditionally employed to determine a "p-value" representing the probability that random chance could explain the result In general, a 5% or lower p-value is considered to be statistically significant Psychologists look for a probability of 5% or less that the results are do to chance This means there is a 95% chance the results are not due to chance

Frequency distributions a mathematical function showing the number of instances in which a variable takes each of its possible values. A visual showing how many times a number occurs What would this look like on a bar graph? How do you know the MODE?

The NORMAL CURVE “the symmetrical bell-shaped curve that describes the distribution of many psychical and psychological attributes. Most scores fall near the average, and fewer and fewer scores lie near the extremes.” 68-95-99.7% RULE

Normal curve Gives us basis for comparison to “norms” or representative groups of people Ex. IQ tests, heights, mental aptitudes Scores are a certain standard deviation from the mean (Z-scores)

Normal curve As you get further to extremes, less scores occur Z-score of 1 OR -1, 34% Z-score of 2 OR -2, 13.5% Z-score of 3 OR -3, 2.5% As you get further to extremes, less scores occur 1 standard deviation off the mean (below and above) = 68% total, 34% each way 1-2 standard deviations away from the mean (either way) = 95% total, 47.5% 3 standard deviations away from the mean (either way) = 99.7%, 49.85% each More than 3 standard deviations away = 0.3% total, 0.15% each way

Normal curve practice What percent of scores fall when Z = +1? What percent of scores fall within -1 and -2 standard deviations below the mean? What percent of scores fall 0 to 3 standard deviations above the mean?